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free energy curves

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Published: 01 March 2012
Fig. 3.19 (a) Molar free-energy curve for the α phase. (b) Molar free-energy curves for α and β. Adapted from Ref 3.1 More
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Published: 01 December 2008
Fig. 3.9 Free-energy curves for an ideal solution and a regular solution of A-B binary system. (a) Ideal solution, Ω AB = 0. (b) Solution with Ω AB < 0 (c) Solution with Ω AB > 0. A concave region appears at the temperature below T C = Ω AB /2 R (see section 4.4 ). More
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Published: 01 March 2012
Fig. 2.12 Gibbs free-energy curves during solidification. Source: Ref 2.2 More
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Published: 01 March 2012
Fig. 2.14 Free-energy curves for homogeneous nucleation. Source: Ref 2.2 More
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Published: 01 June 2008
Fig. 4.3 Gibbs free-energy curves during solidification More
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Published: 01 June 2008
Fig. 4.5 Free-energy curves for homogeneous nucleation More
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Published: 01 June 2008
Fig. 6.14 Gibbs free energy curves and construction of binary phase diagram. Source: Ref 6 More
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Published: 01 June 2008
Fig. 6.15 Gibbs free energy curves and construction of eutectic phase diagram. Source: Ref 6 More
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Published: 01 December 2008
Fig. 3.11 Composition and free-energy curve of a complex oxide (Al, Cr) 2 O 3 . (a) Composition of (Al, Cr) 2 O 3 . (b) Free-energy curve of Al 2 O 3 -Cr 2 O 3 pseudobinary system (schematic illustration) More
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Published: 01 March 2012
Fig. 3.11 The relationship between the free-energy curve for a solution and the chemical potentials of the components. Adapted from Ref 3.1 More
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Published: 01 March 2012
Fig. 9.17 Free-energy curve illustrating change in chemical potential with composition. Source: Ref 9.9 as published in Ref 9.10 More
Series: ASM Technical Books
Publisher: ASM International
Published: 01 March 2012
DOI: 10.31399/asm.tb.pdub.t53420041
EISBN: 978-1-62708-310-2
... energies and chemical potentials, and shows how the equilibrium state of an alloy can be obtained from free-energy curves. binary solid solutions chemical potential Gibbs free energy interatomic bonds phase diagrams single-component systems thermodynamics THERMODYNAMICS is a branch...
Book Chapter

Series: ASM Technical Books
Publisher: ASM International
Published: 01 June 2008
DOI: 10.31399/asm.tb.emea.t52240075
EISBN: 978-1-62708-251-8
.... The major eutectic systems include the aluminum-silicon eutectic system and the lead-tin eutectic system. The chapter discusses the construction of eutectic phase diagrams from free energy curves. It also provides information on peritectic, monotectic, and solid-state reactions in alloy systems...
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Published: 01 March 2012
Fig. 16.9 (a) Gibbs free-energy composition diagram and (b) locus of solvus curves of metastable and stable equilibrium phases in a precipitation sequence. (a) The points of common tangency show the relationship between compositions of the matrix phase (C″, C′, and C eq ) and the various forms More
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Published: 01 March 2012
Fig. 16.12 Free-energy plots of precipitation sequence in aluminum-copper alloys. (a) Free-energy curve with common tangent points for phase compositions in the matrix. (b) Step reductions in the free energy as the transformation proceeds. C eq and C 3 , copper content of α eq and α 3 More
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Published: 01 December 2008
atom. (c) The free energy curve (1273 K) More
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Published: 01 December 2008
Fig. 4.1 Conditional equations of heterogeneous equilibrium in a unitary (a) and a binary (b) system. (a) Intersection of free-energy curves is the equilibrium temperature in a unitary system. (b) Points of contact ① and ② on the common tangent indicate each More
Series: ASM Technical Books
Publisher: ASM International
Published: 01 June 2008
DOI: 10.31399/asm.tb.emea.t52240053
EISBN: 978-1-62708-251-8
... , and in newer texts, the same free-energy curves are now identified with the Gibbs free energy, G . However, what is really important in metallurgical processes is not the free energy, G , itself, but the change in free energy, Δ G . It can be shown that, at constant temperature and pressure: (Eq 4.6) Δ...
Series: ASM Technical Books
Publisher: ASM International
Published: 01 December 2008
DOI: 10.31399/asm.tb.tm.t52320091
EISBN: 978-1-62708-357-7
... materials are explained. 4.1 Basic Rules of Heterogeneous Equilibrium 4.1.1 Common Tangent Law For phase I and II of a one-component system (pure substance A) to be in equilibrium, as in Fig. 4.1(a) , free-energy curves of both phases, G A I and G A I I...
Series: ASM Technical Books
Publisher: ASM International
Published: 01 March 2012
DOI: 10.31399/asm.tb.pdub.t53420015
EISBN: 978-1-62708-310-2
... G L < 0 Fig. 2.12 Gibbs free-energy curves during solidification. Source: Ref 2.2 Immediately below T m , the free-energy change is very small, so solidification occurs slowly, but at larger undercooling or supercooling ( T m – T ), the free-energy change becomes...